PROBLEM 4.79 KNOWN: Bottom half of an I-beam exposed to hot furnace gases. FIND: (a) The heat transfer rate per unit length into the beam using a coarse nodal network (5 ×4) considering the temperature distribution across the web is uniform and (b) Assess the reasonableness of the uniform web-flange interface temperature assumption. SCHEMATIC: ASSUMPTIONS: (1) Steady-state, two-dimensional conduction, and (2) Constant properties. ANALYSIS: (a) The symmetrical section of the I-beam is shown in the Schematic above indicating the web-flange interface temperature is uniform, Tw= 100°C. The nodal arrangement to represent this system is shown below. The nodes on the line of symmetry have been shown for convenience in deriving the nodal finite-difference equations. Using the IHT Finite-Difference Equations Tool, the set of nodal equations can be readily formulated. The temperature distribution (°C) is tabulated in the same arrangement as the nodal network.

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